A Novel Network DEA Model Based on the Directional Distance Function for Simultaneous Handling of Negative and Integer-valued Data

Azizi, Hossein; Rashid, Somayyeh

doi:10.48311/mri.2026.28272

A Novel Network DEA Model Based on the Directional Distance Function for Simultaneous Handling of Negative and Integer-valued Data

Document Type : Original Article

Authors

Hossein Azizi

Somayyeh Rashid

Department of Applied Mathematics, PaM.C., Islamic Azad University, Parsabad Moghan, Iran

10.48311/mri.2026.28272

Abstract

Data Envelopment Analysis (DEA), as a non-parametric and data-driven methodology, is an effective tool for assessing the relative efficiency of a set of decision-making units (DMUs) with multiple inputs and outputs. However, classical DEA models disregard the internal structure of DMUs and treat them as “black boxes.” To overcome this limitation, network DEA has been developed to explicitly model the internal interactions among the components of each DMU. Moreover, in many real-world applications, certain input, output, or intermediate variables are inherently discrete and take integer values, and negative data may also be present. Such characteristics are typically ignored in conventional DEA models and can lead to inaccurate or impractical efficiency estimates. This paper proposes a novel network DEA model based on the directional distance function for two-division series systems, capable of simultaneously handling negative data and integer-valued variables. By defining an appropriate direction vector, the proposed model enables the measurement of system efficiency under both constant returns to scale and variable returns to scale. To demonstrate the capabilities of the proposed model, a real case study involving 29 Iranian supply chains in the medical consumables industry is conducted. The results show that the proposed model not only accurately distinguishes between efficient and inefficient DMUs but also provides projection points that specify the exact pathway for performance improvement in each division. The findings indicate that the proposed approach can serve as a robust and reliable tool for evaluating and enhancing supply chain efficiency, particularly in sensitive industries such as medical consumables.

Keywords

Data Envelopment Analysis (DEA)

Network DEA

Directional Distance Function (DDF)

Negative data

Integer-valued data

Supply chain

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